For two positive real numbers $x>0,y>0$ is there a way to simplify the following function? $$ \ln\left[ \Gamma\left( i x \right) \right] - \ln\left[ \Gamma\left( i y \right) \right] $$
I am tempted to put them into a single logarithm $\ln\left( \frac{\Gamma\left( i x \right)}{\Gamma\left( i y \right)} \right)$ but I don't think I can do this since the arguments of the logarithm are complex.